We used a power-law model \(\varphi _c(f) = af^b\)  to describe the observed frequency-dependent behavior of the coating internal friction [1]}, [2]}, [3]}, and applied least-squares linear regression in order to fit the data. Best-fit parameters are presented in Table REF . It is worth noting that the \(b\)  parameter increased after each annealing step, implying lower loss values in the most sensitive region (50-300 Hz) of GW detectors. Thus, by extrapolating our results to lower frequency, we obtain a loss angle of \(1.8 \times 10^{-4}\)  at 100 Hz for the Ta\(_2\) O\(_5\) -ZrO\(_2\)  annealed at 700 \(^\circ \) C. This value has to be compared to \(2.4 \times 10^{-4}\)  for the Ta\(_2\) O\(_5\) -TiO\(_2\)  layers of GW detectors [4]}.
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